Keyframing Physics Animation
Ensuring that blender is set to "Blender Game" mode, ensure that the "record animation" check box is ticked in the Game menu.


Then hit 
P to start running the game (it'll probably run slower than normal). After the length of the animation you want to record has been recorded, press Esc to exit playing the game. Press left/right on your keyboard, and you'll notice a key frame has been added to each object for every frame of the animation:



(Also notice that if you play the animation using AltA now, the physics will run as it does in the game engine as the position data has been applied to the objects using key frames).

If you want to delete part of this animation or shift all of the physics animation in time, enter the dope sheet window like so:



You can select key frames by pressing B and drawing a box around the key frames you want to select. When doing so, ensure that you select the key frames of the object that you want to edit the animation of, and not X,Y,Z location and rotation as that will distort the physics simulation. You can ensure you are not doing so by clicking on the arrows so that these options are not visible:



After you have selected the key frames of the object you want to edit, you can increase/decrease the speed of the animation using the S key and make the animation of that object occur later/earlier in time using the G key.



You can also delete parts of the animation by box selecting the key frames you want to delete from the animation as outlined above, and pressing the Del key:



This will mean that the key frames of the object's animation you have deleted will not run (essentially cropping the start and end of the physics simulation if that is desired)